Business Statistics. Syllabus. General Certificate of Education (Advanced Level) Grade 12 and 13 (Implemented from 2017)

Transcription

1 Business Statistics Syllabus General Certificate of Education (Advanced Level) Grade 12 and 13 (Implemented from 2017) Department of Commerce Faculty of Science and Technology National Institute of Education

2 Business Statistics Grade 12 and 13 - syllabus National Institute of Education First print 2017 ISBN : Department of Commerce Faculty of Science and Technology National Institute of Education Printed by :

3 Content Pages 1.0 Introduction i 2.0 National Goals iii 3.0 Basic Competencies iv - v 4.0 Objectives of the syllabus vi 5.0 Relationship between the common national goals and the objectives of the syllabus vii 6.0 Syllabus Grade 12 syllabus Grade 13 syllabus School policies and programs Assessment and evaluation i

4 1.0 Introduction The subject " Business Statistics" is introduced to the General Certificate of Education (Advanced Level) with the education reforms of It is no secret that a majority of students pursuing G.C.E. (A/L) in Sri Lanka select of subjects outside the science stream. This subject was introduced as the result of realization by academics, involved in the reforms activities, in the field of education, regarding the absence of quantitative techniques in the Arts and Commerce streams conducive to the development of skills related to Mathematics and Measurement. In a social system, advancing day by day in co-operation with the challenges of technological methodologies, it is essential that the capability to arrive at correct and effective decisions is an attribute that should be developed in every individual. Through the introduction of this syllabus, it is expected to equip the majority of those completing their senior secondary education through Arts and Commerce as well as Technology streams, with skills related to mathematics and measurement, when they join the mainstream of society. This subject is nurtured by a number of superior scientific methodologies that will contribute to the minimization of the risk of uncertainty in the utilization of one s resources frugally and in an economically effective manner in the achievement of an outstanding product. Similarly, the subject statistics occupies an important place in universally accepted professional courses like AAT, SLIAC, CIMA, ACCA. Therefore, the study of business statistics by any student sitting one s G. C. E. (A/L) s through the Arts/Commerce/ Technology streams stands to benefit in numerous ways in the future. The business statistics syllabus, introduced in 1995 has been subject to revision on two occasions to be implemented from The present revised syllabus, anticipates student attention to be focused on the involvement of computer technology and methods of electronic data collection in the organization and analysis of data in place of outdated methodologies, in order to overcome the challenges of the modern world. Therefore, it is expected that the pursuit of Business Statistics will prove of immense service to the future of any student studying science, Arts, Commerce and Technical streams at G.C.E. (A/L)s. i

5 2.0 National Goals (i) National building and the establishment of a Sri Lankan identity through the promotion of national cohesion, national integrity, national unity, harmony, and peace, and recognizing cultural diversity in Sri Lanka s plural society within a concept of respect for human dignity (ii) (iii) (iv) (v) (vi) (vii) (viii) Recognizing and conserving the best elements of the nation s heritage while responding to the challenges of a changing world Creating and supporting an environment imbued with the norms of social justice and a democratic way of life that promotes respect for human rights, awareness of duties and obligations, and a deep and abiding concern for one another Promoting the mental and physical well-being of individuals and a sustainable life style based on respect for human values Developing creativity, initiative, critical thinking, responsibility, accountability and other positive elements of a well-integrated and balanced personality Human resource development by educating for productive work that enhances the quality of life of the individual and the nation and contributes to the economic development of Sri Lanka Preparing individuals to adapt to and manage change, and to develop capacity to cope with complex and inforeseen situations in a rapidly changing world Fostering attitudes and skills that will contribute to securing an honorable place in the international community, based on justice, equality and mutual respect iii

6 3.0 Basic Competencies The following Basic Competencies developed through education will contribute to achieving the above National Goals. (i) Competencies in Communication Competencies in Communication are based on four subsets: Literacy, Numeracy, Graphics and IT proficiency. Literacy : Listen attentively, speck clearly, read for meaning, write accurately and lucidly and communicate ideas effectively Numeracy : Graphics : Use numbers for things, space and time, count, calculate and measure systematically Make sense of line and form, express and record details, instructions and ideas with line, form and color IT proficiency : Computeracy and the use of information and communication technologies (ICT) in learning, in the work environment and in personal life (ii) Competencies relating to Personality Development - General skills such as creativity, divergent thinking, initiative, decision making, problem solving, critical and analytical thinking, team work, inter-personal relations, discovering and exploring - Values such as integrity, tolerance and respect for human dignity - Emotional intelligence (iii) Competencies relating to the Environment These competencies relate to the environment : social, biological and physical. Social Environment : Awareness of the national heritage, sensitivity and skills linked to being members of a plural society, concern for distributive justice, social relationships, personal conduct, general and legal conventions, rights, responsibilities, duties and obligations Biological Environment : Awareness, sensitivity and skills linked to the living world, people and the ecosystem, the trees, forests, seas, water, air and life-plant, animal and human life iv

7 Physical Environment : Awareness, sensitivity and skills linked to space, energy, fuels, matter, materials and their links with human living, food, clothing, shelter, health, comfort, respiration, sleep, relaxation, rest, wastes and excretion included here are skills in using tools and technologies for learning, working and living. (iv) Competencies relating to Preparation for the World of Work. Employment related skills to maximize their potential and to enhance their capacity to contribute to economic development, to discover their vocational interests and aptitudes, to choose a job that suits their abilities, and to engage in a rewarding and sustainable livelihood. (v) Competencies relating to Religion and Ethics Assimilating and internalizing values, so that individuals may function in a manner consistent with the ethical, moral and religious modes of conduct in everyday living, selecting that which is most appropriate. (vi) Competencies in Play and the Use of Leisure Pleasure, joy, emotions and such human experiences as expressed through aesthetics, literature, play, sports and athletics, leisure pursuits and other creative modes of living (vii) Competencies relating to learning to learn Empowering individuals to learn independently and to be sensitive and successful in responding to and managing change through a transformative process, in a rapidly changing, complex and interdependent world. v

8 4.0 Objectives of the syllabus ² Motivating for efficient utilizations of resources through a systematic analysis of business data ² Guiding for generalization in connection with the entirety by analyzing a representative portion ² Leading towards risk minimizing and optimal decisions ² Directing one to forecast prospective trends of a variable scrutinizing in the current business affairs ² Stimulating one to approach new trends in business through involvement in research and development affairs in the business field ² Preparing to overcome the challenges one comes across in job-oriented higher education field ² Inculcating application of modern technology for a efficient analysis of data ² Encouraging the individual to face the unemployment problem successfully by promoting entrepreneurship skills ² Inspiring one to lead a balanced life style behaving as a rational customer ² Leading towards higher education in the field of statistics by enhancing statistics literacy vi

9 5.0 Relationship between the common national goals and the objectives of the syllabus Objectives of the syllabus Common National Goals i ii iii iv v vi vii viii ² Motivating for efficient utilizations of resources through a systematic analysis of business data ² Guiding for generalization in connection with the entirety by analyzing a representative portion ² Leading towards risk minimizing and optimal decisions ² Directing one to forecast prospective trends of a variable scrutinizing in the current business affairs ² Stimulating one to approach new trends in business through involvement in research and development affairs in the business field ² Preparing to overcome the challenges one comes across in job-oriented higher education field ² Inculcating application of modern technology for a efficient analysis of data ² Encouraging the individual to face the unemployment problem successfully by promoting entrepreneurship skills ² Inspiring one to lead a balanced life style behaving as a rational customer ² Leading towards higher education in the field statistics by enhancing statistics literacy vii

10 Proposed plan in the allocation of competency levels in the syllabus into the school terms Grade Term competency and competency level No. of periods No. of competency levels First term From competency level 1.1 to competency competency levels level 3.3 Grade 12 Second term From competency level 3.4 to competency level competency levels Third term From competency level 5.11 to competency competency levels level 6.3 First term From competency level 7.1 to competency competency levels level 7.11 Grade 13 Second term From competency level 8.1 to competency level competency levels Third term From competency level 9.8 to competency competency levels level

11 6.0 Syllabus Grade 12 Syllabus Grade 13 Syllabus Competency No. of Competency No. of 1.0 Studies the scope and the nature of the subject Business Statistics Uses statistical estimation for business decision making Organises and presents business data Uses statistical hypothesis testing for business decision making Analyses business data using the techniques of descriptive statistics Analyses the time dependent variables and forecasts Forecasts, having studied the relationships between the variables. 5.0 Demonstrates the preparedness to face business risk Uses Statistical Quality Control techniques for management decision making Uses indices for making business Uses appropriate sampling techniques for collecting data to make business decisions. 32 decisions

12 6.1 Grade 12 Syllabus Competency Competency Level Content Learning Outcomes Studies the scope and the nature of the subject Business Statistics. 1.1 Reviews Business Statistics and its limitations. Statistics Definition Business Statistics Function Limitations Importance of statistics Categories of statistics Descriptive Statistics Inferential Statistics Defines Statistics. Explains the functions of Business Statistics. Differentiates between Descriptive Statistics and Inferential Statistics. Points out the importance of statistics. Explains the limitations of statistics. Describes the misuses of statistics. 04 Misuses of statistics 1.2 Analyses the contribution of Statistics to the business field. Contribution of statistics to the business field Specific uses of Business Statistics For market surveys and research For production planning and quality control For financial management For human resource management For Research and Development Contribution of statistics in other subjects. Highlights the situations where statistics is important in the business field. Lists the various techniques used in statistics. Explains how to use these techniques in various business situations. Evaluates the contribution of statistics in other field. 04

13 . 2.0 Organises and presents business data. 2.1 Studies various sources of collecting data. Introduction to data Population and sample Categories of data Quantitative data Qualitative data Internal data External data Sources of data Primary data Secondary data Scales of measuremets Nominal scale Ordinal scale Interval scale Ratio scale Introduces statistical data. Describes the need of data for statistical studies. Introduces population. Introduces sample. Introduces quantitative data and gives examples. Introduces qualitative data and gives examples. Introduces internal data and gives examples. Introduces external data and gives examples. Introduces primary data sources and secondary data sources and differentiates between them. Points out the reliability of primary data sources. Points out the advantages and disadvantages of primary data. Lists the sources of secondary data. Points out the advantages and disadvantages of secondary data. Categorices data according to the scale of measurements

14 2.2 Constructs the instruments required to collect data. Methods of collecting data Personal Interviews Self enumeration (postal questionnaire method) Telephone interviews Direct observation Electronic data collecting Focused group interviews Merits and demerits of data collecting methods Instruments of collecting data Schedule Questionnaire Pre-test Editing of data Introduces the methods of collecting data. Explains the personal interview method. Shows the merits and demerits of the personal interview method. Explains the self enumeration method. Explains the merits and demerits of the self enumeration method. Introduces the telephone interview method. Shows the merits and demerits of the telephone interview method. Explains how to collect data through the direct observation method. Shows the merits and demerits of the direct observation method. Explains the electronic data collection method. States how to collect data using focused groups. Analyses the instruments of collecting data comparatively. States the facts to be considered in preparing the schedule and questionnaire. Explains the pre test. Introduces the editing of data and explains the requirements of its. 10

15 2.3 Organises business data. Organisation of business data Organised data Explains the difference between raw data and organized data. 12 Array of data Prepares the array of data. Stem and leaf diagram Shows the merits and demerits of the array Tabulation of data. Construct the stem & leaf diagram. Frequency distribution Ungrouped frequency distribution Grouped frequency distribution Relative frequency distribution Cumulative frequency distribution Cumulative relative frequency distribution Explains the merits and demerits of stem & leaf diagram. Names the properties of a complete table. Presents the data in a complete table. Constructs the ungrouped and grouped frequency distributions by given data. Constructs the relative frequency distribution and cumulative frequency distribution for a given frequency distribution. Constructs the cumulative relative frequency distribution using a relative frequency distribution.

16 2.4 Presents business data Presentation of data using charts Simple bar charts Describes the facts to be considered in construction of a chart. 12 using charts. Component bar charts Points out the need for charts by means Multiple bar charts of presentation of data. Pictograms Introduces the simple bar chart. Pie-charts Points out the need of simple bar charts. Profile charts Constructs a simple bar chart using the given data. Introduces the component bar chart. Points out the need of a component bar chart. Constructs a component bar chart using the given data. Introduces the percentage component bar chart. Introduces the multiple bar chart. Points out the need for a multiple bar chart. Constructs a multiple bar chart using given data. ntroduces the pictogram. Points out the need of a pictogram. Construct a pictogram for given data. Introduces the pie chart.

17 Points out the need of a pie chart. Constructs a pie chart using the given data. Introduces the profile chart. Points out the need of a profile chart. Constructs a profile chart using the data given. points out the problems arising in presenting data using charts. Explains the merits and demerits of each technique of represntation of data. 2.5 Presents business data using graphs. Presentation of data using graphs Linear graphs Histogram Frquency polygon Cumulative frequency curve (Ogive curve) Processes data in an appropriate manner to be presented graphically. Constructs linear graphs naming the axes appropriately. Describes the deviations of data using linear graphs. Constructs the histogram and the frequency polygon related to the 12 frequency distribution. Differentiates between the histogram and the frequency polygon.

18 Constructs the ogive curve using the cumulative frequency distribution. States the median observing the ogive curve. 2.6 Constructs specific graphs for presentation of business data. Lorrenze Curve Construction of the Lorrenze curve Interpretation of the Lorrenze curve Ginnie coefficient Applications of the Lorrenze curve Z - chart Introduces the variables that can be represented using the Lorrenze curve. Constructs the Lorrenze curve by processing the data appropriately. Explains the inequity distribution of relevant variable using the Lorrenze curve. Describes how to compute the Ginnie co-efficent for making decisions. 08 Construction of the z - chart States the instances for the Lorrenze curve Applications of the z - chart is applicable. Introduces the variables that can be represented by using a z - chart. Interprets the z - chart. Constructs z - chart processing the data appropriately. Describes the uses of the z - chart in decision making.

19 Analyses business data using the techniques of descriptive statistics. 3.1 Uses the measures of central tendency for data analysis. Central tendency Measures of central tendency for ungrouped and grouped data Mean Median Mode Properties of a good measure of central tendency Relative merits and demerits of major measures of central tendency Interprets central tendency. Explains the properties of a good measure of central tendency. Interprets the Mean as a measure of central tendency. Computes the mean for ungrouped and grouped data. Interprets the Median as a measure of central tendency. Computes the Median for ungrouped and grouped data. Interprets the Mode. Computes the Mode for ungrouped and grouped data. Lists the significant features of Mean as a good measure of central tendency. Lists the significant features of Median Lists the significant features of Mode. 12 Comparatively explains the relative advantages and disadvantages of measures of central tendency.

20 Provides examples for specific situations where each measure of central tendency is applicable. Explains the Empirical relationship inbetween Mean, Median and Mode. 3.2 Analyses data using specific measures of central tendency. Specific measures of central tendency Geometric mean Harmonic mean Weighted mean Points out the need of specific measures of central tendency for data analysis. Interprets the geometric mean. Explains the situations where the geometric mean is applicable. Computes the geometric mean for 12 given data. Points out the problems arrisen in computing the geometric mean. Interprets harmonic mean. Explains the situations where the harmonic mean is applicable. Computes the harmonic mean. Interprets weighted mean Describes what weighting means. Explains the situations where the weighted mean is applicable.

21 Computes the weighted mean. Arrays, the geometric mean, harmonic mean and the simple arithmetic mean of the same data set in accordance with the magnitude of each measure. Makes business decisions using the mearures of central tendency. 3.3 Uses. the measures of relative location to analyse the location of data. Relative location Measures of relative location Quartiles Decimals/Deciles Percentiles Measures of relative location for ungrouped and grouped data Introduces, relative location. Describes the measures of relative location. States the benifits of computing the relative location numerically. Computes the quartiles, decimals and percentiles of ungrouped and grouped distributions. Makes decisions using quartiles, deciles and persontiles. 12

22 3.4 Uses the measures of dispersion for data analysis. Dispersion Interpretation Importance Measures of dispersion Range Quartile deviation Mean deviation Variance Standard deviation Measures of relative dispersion Co-efficient of variation Standardized marks (Z-score) Interprets dispersion. States the uses of computing dispersion. Lists the measures used to measure dispersion. Computes measures such as the Range, Quartile Deviation, Mean Deviation, Variance and the Standard Deviation of ungrouped and grouped frequency distributions. Introduces relative dispersions. Explains the need of measuring relative dispersion. 12 Measures relative dispersion using the co-efficient of variation. Standardizes the data using the Z-value. Makes business decisions using the measures of dispersion.

23 3.5 Uses the measures of skewness and kurtosis for data analysis. Skewness Interpretation Measures of skewness Pearson s the 1 st co-efficient of skewness Pearson s the 2 nd co-efficient of skewness Bowley s the 1 st co-efficient of skewness Bowley s the 2 nd co-efficient of skewness Kurtosis Interpretation Types of Kurtosis Leptokurtic Mesokustic Platykurtic Interprets the skewness and points out the need of it. Interprets and computes pearson s 1 st co- efficient of skewness. Explains the situations where the pearson s 1 st co-efficient of skewness is applicable and inapplicable. Interprets and computes Pearson s 2 nd co-efficient of skewness. Explains the situation s where the Pearson s 2 nd co-efficient of skewness is applicable and inapplicable. Interprets and computes the Bowley s 1 st co-efficient of skewness. Points out the good qualities and weaknesses of Bowley s 1 st co-efficient of skewness. 12 Measures of kurtosis Percentage kurtosis co-efficient Box & Whisker Plot Construction Interprets and computes Bowley s 2 nd co-efficient of skewness. Points out the good qualities and weaknesses of Bowley s 2 nd co-efficient of skewness. Application

24 Interprets the nature of the distribution using the co-efficient of skewness. Introduces Kurtosis and points out the need of it. Explains the situations of Kurtosis such as Mesokustic, Leptokurtic and Platykurtic. Interprets and computes the percentage Kurtosis co-efficient. Interprets the nature of the distribution using the co-efficient of Kurtosis. Introduces the Box & whisker plot and the need of it. Constructs a Box & Whisker plot for a given data set and describes the nature of dispersion of these data.

25 4.0 Forecasts, having studied the relationships between the variables. 4.1 Classifies the variables in accordance with the nature of relations. Variables Independent variables Dependent variables Scatter diagrams Relationship between the variables Linear relationships. Linear positive relationships. Linear negative relationships. Non-linear relationships. Instances which are not related Interprets the variables. Names the variables which are related to each other. Differentiates between the independent variables and dependent variables. Introduces the scatter diagram. Presents the data using a scatter diagrams. Explains the linear relations between variables using scatter diagrams Points out the non linear relations between the variables using scatter diagrams. Presents a situation where there is no relations between the variables using a scatter diagram. Describes the uses of a scatter diagram.

26 4.2 Studies the linear correlation concept between two variables. Concept of the linear correlation Introduction Uses Interprets the concept of correlation. Provides with the instances where the correlation is applied. Describes the uses of knowing the correlation between two variables. 04 Explains the need of measuring the size of correlation between two variables. 4.3 Quantifies the Product Moment Correlative Co-efficient. Product Moment Correlative Co-efficient Introduction Computing Interpretation Interprets the product moment correlative co-efficient. Gives examples for situations where the product moment correlative co-efficient is applied. 06 Computes the value of product moment correlative co-efficient for a given pair of variables. Points out the properties of the product moment correlative co-efficient. Explains the size and the direction of the correlation between two variables with the various values taken by the co-efficient.

27 4.4 Quantifies the Rank Correlative Co-efficient. Rank Correlative Co-efficient Introduction Computing Interpretation Ranks the variables which are not quantitative. Interprets the rank correlative co-efficient. 04 Gives examples for the situations where the rank correlative co-efficient is applicable. Computes the rank correlative co-efficient between two variables which are not quantitative. Explains the characteristics of the rank correlative co-efficient. Describes the association among the two variables using the co-efficient. Ranks the quantitative variables. Examines the association between the ranked quantitaive variables. 4.5 Studies the concept of regression. Concept of regression Introduction Simple regression Multiple regression Population regression model Estimated regression model Uses of regression Distinguishes between deterministic models and stochastic models. Explains the requirement of expressing the dependent variable with respect to the independent variable using an equation (model). 06

28 Interprets the regression. Distinguishes the simple regression and multiple regression. Gives examples for situations where simple regression and multiple regression are applicable. Writes the population regression model. Introduces the variables, co-efficients and the error term of the population regression model. Writes the estimated regression model. Introduces the variables and co-efficients of the estimated regression model. Describes the uses of regression. 4.6 Uses the Free Hand Method to fit a simple regression Line. Free Hand Method Introduction Fitting the line Importance Weakpoints Introduces the free hand method. Fits a regression line on the free hand method. Drows the regression line on the scatter diagram using the given data. 02 States the merits and demerits of deriving a regression line on the free hand method.

29 4.7 Uses the Least Square Method to fit a simple regression line. Least Square Method Introduction Fitting the regression line Importance Introduces the least square method. Derives the equation of the regression line on least square method for given data. Describes the regression co-efficient. 04 Weakpoints Estimates the dependent variable on the indpendent variable using the regression line. States the merits and demerits of fitting a regression line on the least square method. 4.8 Tests the goodness of fit of a regression line. Testing the goodness of fit of a regression line Co-efficient of determination Introduction Calculation Interpretation Interprets the co-efficient of determination. Computes the co-efficient of determination using a regression line that has been fit. Describes about the goodness of fit of the 08 Forecasting the dependent variable using the estimated regression line regression line using the computed co-efficient of determination. Estimates the value of dependent variable using the estimated regression line for any given value of the independent variable.

30 5.0 Demonstrates the preparedness to face business risk. 5.1 Analyses the concept of probability related to business uncertainty. Probability Definition Events Certain events Uncertain events Impossible events Defines probability as a statistical technique of measuring uncertainty. Lists business events. Explains the certain (definite) events involved in businesses. Explains the uncertain events involved in businesses. Explains the impossible events that never happen Seperates the random experiments. Deterministic experiments Random experiments Sample space Trails Differentiates between deterministic experiments and random experiments. Provides appropriate examples for deterministic experiments and random experiments. 02 Highlights the instances related to random experiments from the business field. Interprets the sample space. Presents the sample space using sets, tree diagrams, and pictograms. Explains trails.

31 5.3 Uses sets notations to combine events. Events Event space Simple events and composite events Making the events composite Union Intersection Complement of an event Difference of two events Interprets the events. Separates the sample space into regions that belong to each event interpreted in it. Interprets simple events. Interprets composite events. Explains that a composite event consists of several simple events. Makes the events composite using the union and intersection of sets. 04 Expresses the complement of an event using venn diagrams and standard symbols. Expresses the difference between two events using venn diagrams and standard symbols. Interprets the event space.

32 5.4 Prepares and chooses a set of materials. Counting techniques Permutations Combinations Tree diagrams States the number of ways in which a set of different materials can be arranged in order. Interprets the permutations and combinations 04 Writes the formula used to compute a number of permutations and combinations. Differentiates between permutations and combinations. Solves problems accurately using the relevant formulae. Derives the sample space for random experiments using tree diagrams. Solves problems related to random experiments using tree diagrams. 5.5 Bionomial theorem Expresses a binomial expression. 04 Expands a binomial expression. Bionomial expansion Usage of bionomial theorem Expands a binomial expression. States that a binomial expression with any power can be expanded. Uses the binomial theorem to binomial expansion.

33 5.6 Classical approach Interprets the classical approach. 02 Uses the classical approach as an approach to probability. Interpretation Usage Points out the situations where the classical approach is applicable to evaluate probability. Computes the probability of an event in accordance with the classical approach. Points out the weaknesses in the classical approach. 5.7 Uses the relative frequency approach as an approach to probability. Relative frequency approach Interpretation Usage Expresses relative frequency accurately. Represents graphically the relative frequency of occurrence of the considered event with respect to each number of times that the experiment is conducted. 04 Interprets the probability based on the relative frequency of occurrence of the considered event when increasing the number of times that the experimnt is conducted. States the situations where the relative frequency approach can be applied.

34 5.8 Uses the subjective approach as an approach to probability. Subjective approach Interpretation Uses Explains the subjective approach. Points out the instances where the probability is expressed on subjective approach. Points out the weaknesses of this approach as a technique of expressing the probability Uses the axiomatic approach as an approach to probability. Axiomatic approach Interpretation Theorem Uses States the axioms related to probability. Writes expressions for probability of various events using axioms. Interprets the additive law of probability. Interprets the mutually exclusive events. States the additive law for the union of mutually exclusive events. States the additive law for the union of any two events. Solves probability based problems using the additive law. Uses venn diagrams as well as the theorems to calculate the probability of various events. Makes rational decisions by computing the possibilities of various events. 06

35 5.10 Conditional probability Interprets the conditional probability. 04 Uses the techniques of conditional probability to solve the probability based problems. Interpretation Multiplicative law Uses Solves problems related to the conditional probability using the relevant formula. States the multiplicative law using the fomulae of the conditional probability. Demonstrates the ability of making rational decisions in the business field using the concept of conditional probability Uses the probability theorems of independence to solve problems. Independence Interpretation Independence of two events Independence in more than two events Uses of independence Interprets independence. Separates the independent events through various events. Uses the probability theorems of independence to make business decisions. Computes the probability of occurring the independent events simultaneously. 04 Computes the probability of occurring more than two independent events simultaneously.

36 5.12 Apportions sample space correctly to use the total probability theorem and Baye s theorem. Apportionment of the sample space Total probability theorem Interpretation Uses Explains the mutually exclusive and collectively exhaustive events. Highlights the events that provide the basis for total probability theorem. Interprets the total probability theorem. 08 Baye s theorem Interpretation Uses Usage of tree diagrams to solve problems Gives examples for the instances where the total probability theorem is applicable. Computes the probability using the total probability theorem. Interprets the Baye s theorem. Gives examples for instances where the Baye s theorem is applicable. Solves problems using the Baye s theorem Uses tree diagrams to solve problems related to probability. Builds up probability distributions interpreting the random variables Random variables Discrete random variables Continuous random variables Probability distributions Introduces the random variables. Categorizes the random variables. Gives examples for discrete random variables. 08 Definition Gives examples for continuous random variables.

37 Expected value Introduces the probability distribution. Variance computing the expected value and the variance of a discrete random variable Explains the conditions that should be satisfied by a probability distribution. Introduces the expected value and the variance of a probability distribution of a random variable. Builds up the probability distribution of a discrete random variable related to a random experiment. Computes the expected value and the variance of a discrete probability distribution. Makes business decisions using probability distribution of a discrete random variable. Studies the Standard Probability Models. Standard Probability Models Interpretation Discrete Probability Models Continuous Probability Models Explains the necessity of the standard probability models. Lists out the probability models related to discrete random variables. Names the probability models related to continuous random variables. 04

38 Solves probability based problems using the binomial distribution Solves the probability based problems using the poisson model. Bionomial Distribution Bernoli trials Conditions relevant to the bionomial distibutions Probability mass function of a bionomial distribution Mean and variance of a bionomial distribution Uses of the bionomial distribution model Properties of a binomial distribution Poisson Distribution Introduction to poisson distribution Probability mass function of a poisson distribution Mean and variance of a poisson Describes Bernoli trials. Interprets the bionomial distribution stating the relevant conditions. Provides instances for binomial random variables using binomial theorem. Interprets the function of the binomial distribution. Solves probability based problems using the function of a binomial distribution. Uses the binomial distribution tables to solve the problems easily. Interprets and computes the mean and the variance of a binomial distribution. Describes the properties of a binomial distribution. Writes the assumptions on which the poisson random variables have been built. Interprets the poisson distribution. Provides instances for possison random variables. Writes the probability mass function of the poisson distribution

39 distribution Usage of the poisson model Properties of a poisson distribution Poisson approximation to the binomial distribution Explains the mean and the variance of the poisson distribution. Describes the properties of a poisson distribution. Solves problems related to poisson distribution easily using the tables. States the conditions needed to use the poisson distribution as an approximation to the binomial distribution. Uses the poisson distribution as an approximation to solve the problems related to the binomial distribution Studies the normal distribution as a probability model. Normal Distribution Introduction Probability density function of the normal distribution Mean and variance of the normal distribution Properties of the normal distribution Points out the characteristics of a normal distribution and defines it. Defines the probability density function of the normal distribution. States the parameters of a normal distribution. Provides instances for variables which distribute normally. 06

40 5.18 Uses the standard normal distribution to solve the probability related problems. Standard Normal Distribution Introduction Probability density function of the standard normal distribution Transformation of a normal distribution into a standard normal distribution Properties of the standard normal distribution Solves problems using the standard normal distribution tables Normal distribution as an approximation to the binomial distribution Normal distribution as an approximation to the poisson distribution Introduces the standard normal distribution. States the probability density function of the standard normal distribution. Transforms a normal distribution to the standard normal distribution. Lists out the properties of a standard normal distribution. Differentiates between the normal distribution and the standard normal distribution. Solves problems using the standard normal distribution tables. Solves problems related to the binomial distribution using the normal approximation. Solves problems related to poisson distribution using the normal approximation 14 Explains the importance of a normal distribution.

41 6.0 Uses appropriate sampling techniques for collecting data to make business decisions. 6.1 Plans a sample survey for statistical inference. Statistical inference Population and sample Parameters and statistics Census and sample survey Sampling frame and sampling unit Sampling with replacement and without replacement Merits and demerits of a sample survey Basic steps of a sample survey Sampling errors and non-sampling errors Introduces statistical inference. Differentiates between population and sample. Differentiates among census (complete enumeration) and sample survey. Differentiates between the parameters and statistics. Explains sampling. Describes the sampling frame and the sampling unit. Differentiates between sampling with replacement and sampling without replacement Explains the need of a sample survey. Describes the advantages of a sample survery beyond a census. Proposes the most appropriate sampling frames to draw out various samples.

42 Gives instances where sample surveys should not be followed. Lists out the steps of a sample survey. Introduces the sampling error. Introduces the non-sampling errors. Reasonifies for non-sampling errors. 6.2 Uses probabilistic sampling techniques for alternative sampling. Probabilistic sampling techniques Simple random sampling Introduction Selecting the sample Usage of the sampling technique Merits and demerits Explains probabilistic sampling. States the situations where probabilistic sampling is applicable. Lists the merits and demerits of probabilistic sampling. Defines the simple random sampling. Selects simple random samples from a finite population. 16 Stratified sampling Introduction Selecting the sample Usage of the sampling technique Merits and demerits Gives examples where the simple random sampling technique can be applied. Lists out the merits and demerits of the simple random sampling technique. Defines the stratified random sampling technique. Selects the stratified random samples from a finite population.

43 Cluster sampling Introduction Selecting the sample Usage of the sampling technique Merits and demerits Systematic sampling Introduction Selecting the sample Usage of the sampling technique Merits and demerits Gives instances where the stratified sampling technique is applicable. Lists the merits and demerits of the stratified sampling technique. Defines the cluster sampling. Describes the concepts related to cluster sampling. Gives instances where cluster sampling is applicable. States the merits and demerits of cluster sampling. Defines one stage, two stage and multi stage cluster sampling separately. Describes how to draw a sample under each technique. Defines the systematic sampling. Lists the steps followed in selecting a systematic sample. Gives instances where systematic sampling is applicable. Describes the relationships between stratified, cluster and systematic samples. Points out the relative merits and demerits of each technique.

44 6.3 Uses non-probabilistic sampling techniques for sampling. Non-probabilistic sampling techniques Quota sampling Introduction Drawing the sample Uses of the sampling technique Merits and demerits Judgement sampling Introduction Drawing the sample Usage of the sampling technique Merits and demerits Convenient sampling Introduction Drawing the sample Usage of the sampling technique Merits and demerits Purposive sampling Introduction Drawing the sample Usage of sampling technique Merits and demerits Explains the differences between probabilistic sampling techniques and non-probabilistic sampling techniques. Names the non-probabilistic sampling techniques. Introduces quota sampling. Selects a sample on quota sampling from a given population. Writes the merits and demerits of quota sampling technique. Defines judgement sampling. States the situations where judgement sampling is appropriated. Draws out a sample using judgement sampling from a given population. Lists the merit and demerit of judgement sampling. Defines convenient sampling. Draws a sample on convenient sampling from a given population. lists the merits and demerits of convenient sampling. Describes purposive sampling. Gives instances of purposive sampling. Points out merits and demerits of purposive sampling

45 Grade 13 Syllabus Competency Competency Level Content Learning Outcomes 7.0 Uses statistical estimation for business decision making. 7.1 Constructs sampling distributions for statistical inference. Sampling distributions Introduction Construction of sampling distributions Introduction of mean and variance of a sampling distribution Builds up probability distributions for statistics. Introduces the probability distribution of a statistic as a sampling distribution. Explains the differences between population distribution, sample distribution and sampling distribution Calculates the mean and variance of a sampling distribution. Explains differences between standard deviatation and the standard error of an estimator. 7.2 Constructs the sampling distribution of the sample mean for statisctical inference. Sampling distribution of the sample mean ( ) When the population is normal Central limit theorem Introduction Sampling distribution of when the population is not normal and the sample size is large Defines the sampling distribution of the sample mean. Constructs the sampling distribution of sample mean of large samples drawn from normal populations with known variance. 18

46 Solving problems related to the sampling distribution of Constructs the sampling distribution of sample mean of large samples drawn from normal populations with unknown variance. Constructs the sampling distribution of sample mean of small samples drawn from normal populations with known variance. Constructs the sampling distribution of sample mean of small samples drawn from a normal population with unknown variance. States the central limit theorem and explains its uses. Constructs the sampling distribution of sample mean of large samples drawn from a population not distributed normally with known variance. Constructs the sampling distribution of sample mean of large samples drawn from a population not distributed normally with unknown variance. Solves the problems related to the sampling distribution of sample mean.

47 Explains that the sampling distributions are inaplicable, when small size samples are drawn form a population that is not normally distributed. 7.3 Constructs the sampling distributions of the difference between two sample means for statistical inference. Sampling distribution of the difference between two sample means 1 2 When the population is normal When the population is not normal and the sample size is large Problem solving related to the sampling distribution of 1 2 Describes what the sampling distribution of the difference between two sample means is. Constructs the sampling distribution of the difference between two sample means. Introduces the mean and the variance of the sampling distribution of the difference between two sample means. 12 Describes the sampling distribution of the difference between two sample means when the populations are normal and variances are known using large samples. Describes the sampling distribution of the difference between two sample means using small samples when the populations are normal with known variance.

48 Describes the sampling distribution of the difference between two sample means when the populations are normal and the variances are unknown using large samples. Describes the sampling distribution of the difference between two sample means when the populations are normal and the variances are unknown using small samples. Describes the sampling distribution of the difference between two sample means for large size samples when the populations are not normal, but the variances are known. Describes the sampling distribution of the difference between two sample means for large samples when the populations are not normal, and the variances are unknown. Solves problems using the sampling distribution of the difference between two sample means. Makes decisions using the sampling distributions of the difference between two sample means.

49 7.4 Constructs the sampling distributions of sample proportions, for satistical inference. Sampling distributions of sample proportions (P) population proportion and sample proportion Sampling distribution of sample proportions (when the sample size is large) Solving problems related to the sampling distributions of sample proportions Explains the population proportion and the sample proportion. Introduces the sampling distribution of sample proportions. Constructs the sampling distribution of the sample proportions. States the mean and the variance of the sampling distribution of the sample proportion. Describes the sampling distribution of the sample proportion when the sample size is large. 08 Solves the problems using the sampling distribution of the sample proportion. Makes decisions related to the sampling distribution of sample proportion.

50 7.5 Constructs the sampling distribution of the difference between two sample proportions for statistical inference. Sampling distribution of the difference between two sample proportions (P 1 - P 2 ) Difference between two population proportions and difference between two sample proportions The sampling distribution of the difference between two sample proportions. (P 1 - P 2 ) (when the sample size is large) Solving problems related to the sampling distribution of the difference between two sample proportions Provides examples of the situations where the difference between two population proportions is needed. Constructs the sampling distribution of the difference between two sample proportions. Derives the mean and the variance of the sampling distribution of the difference between two sample proportions. Writes down the sampling distribution of the difference between two sample proportions. Solves problems related to the sampling distribution of the difference between two sample proportions. 08